Laser-assisted photoemission from surfaces

G. Saathoff,1,* L. Miaja-Avila,1 M. Aeschlimann,2 M. M. Murnane,1 and H. C. Kapteyn1

1Department of Physics and JILA, University of Colorado, Boulder, Colorado 80309-0440, USA2Department of Physics, University of Kaiserslautern, Kaiserslautern D-67663, Germany

�Received 23 November 2007; published 29 February 2008�

We investigate the laser-assisted photoelectric effect from a solid surface. By illuminating a Pt�111� samplesimultaneously with ultrashort 1.6 and 42 eV pulses, we observe sidebands in the extreme ultraviolet photo-emission spectrum, and accurately extract their amplitudes over a wide range of laser intensities. Our resultsagree with a simple model, in which soft x-ray photoemission is accompanied by the interaction of thephotoemitted electron with the laser field. This strong effect can definitively be distinguished from other lasersurface interaction phenomena, such as hot electron excitation, above-threshold photoemission, and space-charge acceleration. Thus, laser-assisted photoemission from surfaces promises to extend pulse duration mea-surements to higher photon energies, as well as opening up measurements of femtosecond-to-attosecondelectron dynamics in solid and surface-adsorbate systems.

DOI: 10.1103/PhysRevA.77.022903 PACS number�s�: 42.50.Hz, 42.65.Ky, 42.65.Re, 79.60.�i

I. INTRODUCTION

The development of high intensity ultrashort laser pulseshas led to new fields of investigation in strong field physicsand nonlinear optics at the extremes of pulse duration, pho-ton energy, and nonlinear response. A number of novel ef-fects have been revealed, including the generation of laser-like beams of xuv light by high-harmonic radiation �1–3�.These beams exhibit low divergence and consist of pulses ofvery short pulse duration—in the femtosecond-to-attosecondregime—making them a very attractive light source for in-vestigating dynamic processes in atoms, molecules, plasmas,materials, and surfaces. To date, high harmonic beams havebeen used extensively in ir-xuv geometries, where a visiblepump pulse excites dynamics and a time-delayed xuv probemonitors changes in the sample. This approach has been suc-cessfully used to study electron relaxation in materials �4–7�,surface-adsorbate dynamics �8�, photoacoustic dynamics �9�,and molecular dissociation �10�. More recently, high har-monics have been used as a pump beam to study x-ray-induced molecular dynamics �11�. Although photon energies�1 keV can be generated using high-harmonic emission, thephoton flux is too low above 100 eV to be employed rou-tinely in experiments. In this range of incident photon ener-gies, the high-harmonic light can photoemit valence elec-trons to high ejected electron energies, well above theionization threshold of the irradiated gas or solid sample.These electrons are essentially free in the continuum, and thephotoelectron energy spectrum then reflects the energy spec-trum in the sample with relatively minor need for furtherinterpretation.

Time-resolved experiments using ultrafast high harmoniclight have also been greatly expanded by the use of laser-assisted strong-field dynamic processes. When an electron isphotoejected in the presence of an intense laser field of larger

than about 1011 W /cm2, the electron is accelerated by thelaser field. If the interaction occurs continuously over severaloptical cycles, the electrons undergo oscillations. This leadsto ponderomotive energy shifts, and, in the presence ofatomic nuclei or solids that can absorb momentum, the gen-eration of sidebands in the photoelectron spectrum corre-sponding to the absorption and stimulated emission of pho-tons from the laser field.

This laser-assisted photoeffect can be considered to resultfrom “dressing” of the free-electron wave function; i.e., theelectron evolves in a state where the free electron is drivenby the ir laser field. These dressed states are known asVolkov waves. Laser-assisted electron dynamics were firstobserved in electron-atom scattering in the presence of astrong CO2 laser field �12�. Later, this process was applied totime-resolved measurements of laser-assisted Auger decay�LAAD� �13� using ultrashort-pulse soft x-ray plasmasources �14�. Laser-assisted photoemission �LAPE� was firstobserved by Glover et al. �15�, using high harmonic sources.In these experiments, atoms are simultaneously irradiated byxuv and intense infrared �ir� light. The presence of the irlaser modifies the xuv photoelectron spectrum. In both cases,LAAD and LAPE, the observation of laser-assisted dynamicsof the emitted photoelectrons or Auger electrons indicatesthe time of their emission. By varying the time delay be-tween the xuv and ir pulses, the LAPE signal provides anexact timing synchronization between the pulses, as well asproviding a cross correlation between the laser and xuvfields. More recently, LAPE and LAAD have been combinedto measure ultrafast core level dynamics in Krypton atoms�16�. In this experiment LAPE provides time zero, whileLAAD yields the emission time behavior of the delayed Au-ger electrons. In this way, the lifetime of an M-shell vacancyin Krypton could be measured directly in the time domain. Ithas also been shown that with xuv pulse durations in thesuboptical cycle domain, LAPE becomes sensitive to the irelectric field rather than the intensity envelope, giving rise tosubfemtosecond resolution in time-resolved experiments�17–21�. Recently, LAPE has been successfully demon-strated with femtosecond xuv pulses from the free-electronlaser FLASH at DESY in Hamburg �22�.

*Present address: Max-Planck-Institut für Quantenoptik, Garch-ing, Germany. Guido.Saathoff@mpq.mpg.de. FAX: �303� 492-5235.

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However, with the exception of two very recent experi-ments �23,24�, laser-assisted photoemission and laser-assisted Auger decay have been observed only in gas-phaseatomic systems. This limits the current applicability of thephysics of laser-assisted dynamics to the study of isolatedatoms or molecules. Furthermore, this limitation also repre-sents a practical limit to the use of LAPE for xuv pulsecharacterization, since both atomic photoionization crosssections and the obtainable photon flux from high-harmonicsources decrease rapidly with increasing photon energy. Theresult has been that, due to the low target densities in the gasphase, current xuv pulse duration measurements are limitedto photon energies below 100 eV. Other approaches for char-acterizing ultrashort xuv pulses, such as the autocorrelationusing two-photon absorption �25,26�, are even more experi-mentally challenging at very high photon energies, and todate have been demonstrated only at photon energies�50 eV.

In a previous Letter, we reported the first experiments toshow that the physics of the laser-assisted photoelectric ef-fect can be extended to solid-state systems �23�. This repre-sents the laser-assisted version of the original manifestationof the photoelectric effect, where photons of energy ��strike a solid surface with work function Wf and result inejection of electrons with energy up to ��−Wf. The goal ofthis current paper is to show that LAPE can be distinguishedfrom other processes and moreover, that it is possible to per-form experiments over a wide range of intensities whereLAPE is the dominant process in strong-field interactionwith solids.

In our work, a clean Pt�111� single crystal was used as thesolid surface, since it exhibits a large density of d states atthe Fermi edge, with a characteristic peaklike structure in thexuv photoelectron spectrum. In the presence of an intenselaser field, sidebands appear in the Pt�111� photoemissionspectrum. We show that the modification of the photoelec-tron spectrum by LAPE can be distinguished from simpleheating of the electrons by the ir beam by varying the laserpolarization, by measuring the mean energy of the photo-ejected electrons and verifying that it does not change, andby successfully fitting the photoelectron spectrum to theory.We also demonstrate that the surface LAPE can be used tomeasure the pulse duration of our xuv beam.

This result is significant for three reasons. First, the sur-face LAPE has the potential to study ultrafast, femtosecond-to-attosecond time-scale electron dynamics in solids and insurface-adsorbate systems—where complex, correlated, elec-tron relaxation processes are expected. This is in contrastwith measurements to date in atomic systems, where dynam-ics are generally only homogeneously broadened and wheretime-domain studies have duplicated information that can beobtained from spectroscopic studies. Second, surface LAPEwill make it possible to characterize lower-flux and higher-energy xuv pulses, because of the orders-of-magnitudehigher density of target atoms on a surface compared with agas—which is typically limited to �1 mbar pressure to al-low for sufficient electron mean free path in the experiment.Finally, this result represents new physics—the extension ofatomic dressed states to surface dressed states is not obvious,because of complex spatially dependent laser electric fieldspresent at the surface.

In the next two sections we discuss laser-assisted photo-emission from atoms and solids, respectively. We then de-scribe our experimental setup, and several effects such asabove-threshold photoemission, the observed sideband struc-ture and its intensity, angle, and polarization dependence. Wealso discuss data on space-charge and hot electron effects,and show that we can operate over a wide parameter rangewhere the laser-assisted photoemission dominates our experi-mental signal.

II. LASER-ASSISTED DYNAMICS IN ATOMS

We recall here the basic picture of strong-field laser-assisted dynamics, for the limiting case where the electronsinteract with the driving ir laser over many optical cycles.The exchange of photons between free electrons and a stronglaser field is forbidden because energy and momentum can-not be conserved simultaneously. The situation changes if aheavy particle such as an atom or molecule or solid are avail-able to balance momentum conservation. As a result laser-induced “free-free” transitions can occur, along with elec-tronic processes such as Auger decay, photoemission, andelectron-atom scattering, where electrons reside in the con-tinuum spectrum of the particle involved. Especially in thefar-from-threshold case, these electrons behave essentially asfree electrons, with a wave function approximately describedby plane waves with momentum p �in atomic units �=e=m=a0=1�, �p�r , t�= �2��−3/2 exp i�p ·r− p2t /2� in the field-free case.

If these electrons are exposed to a strong low-frequencylaser field of vector potential A=A0 cos �irt, the quasifreeelectrons are ponderomotively shifted and undergo transi-tions between continuum states by exchanging photons withthe laser field �Fig. 1�. In the so-called soft-photon limit,where the kinetic energy of the electrons is large comparedto the dressing laser photon energy �Ekin�ir�, the interac-tion can be modeled quasiclassically as an oscillatory motionwith an amplitude A0 /�ir of the electron in the laser field. Byinserting r→r− �A0 /�ir�cos �irt into the plane wave and per-forming a Fourier transform, the electron wave functionbecomes

= exp�i�p · r −p2

2t���

n

Jn�p · E0

�ir2 �exp�− in�irt�� ,

�1�

with E0=�irA0. This can be viewed as a frequency-modulated plane electron wave. The presence of a Besselfunction is a characteristic feature of laser-assisted dynamics.In the soft photon limit, the interaction depends solely on themomentum of the electron as well as on the intensity andfrequency of the dressing laser—but not on properties of thetarget atom. In this approximation, the target atomic potentialonly enables momentum conservation but does not furtherinfluence the spectrum. Quantum mechanically, theSchrödinger equation of a free electron in a strong field issolved by the Volkov wave functions

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�V�r�,t� =1

�2��3/2 exp�ip · r� n=−�

�

Jn�p · E0

�ir2 ,

Up

2�ir�

�exp�− i�p2/2 + Up + n�ir�t� , �2�

which are momentum eigenfunctions. Here Up=E02 /4�ir

2 isthe ponderomotive potential, n is the number of exchangedphotons, and p is the electron momentum for the field-freecase. Here Jn�a ,b� denotes the generalized Bessel functions�27�. For b=0, i.e., negligible ponderomotive potential, theyreduce to the ordinary Bessel functions Jn�a ,0�=Jn�a�.

In the photoelectric effect, an electron is photoemittedfrom a gaseous or solid sample by a high-energy photon �X.In the presence of a sufficiently strong low-frequency laserfield, the photoelectron is emitted into a Volkov state so thatit undergoes the dynamics described by the generalizedBessel function in Eq. �2�. The laser field induces a pondero-motive shift, as well as a redistribution of these electrons intosidebands separated by one photon energy �ir from the origi-nal energy in the kinetic energy spectrum. For high electronkinetic energies and low laser frequencies, this process canbe described in an approximation similar to the “simple-man’s theory” �28�. In this model, LAPE is considered as atwo-step process. The first step is the xuv photoemission ofan electron unaffected by the ir laser field. This is justified atmoderate laser intensities, because the initial ground statesare more tightly bound to the nuclei than the continuum elec-trons, and are thus only slightly affected by the laser field. Inthe second step, the released electron evolves in the laserfield and is unaffected by the target potential. The interactionof the electron with the laser field in the continuum can thusbe described using the Volkov wave function as a final stateof the xuv photoemission process.

In the field-free case, the S matrix for the xuv photoelec-tric effect from a ground state 0=�0�r�eiEbt with the bind-ing energy Eb into the final state �p of momentum p is thengiven by

�S − 1� fi = − i−�

�

dt��p�AX�t� · p� 0 , �3�

where AX�t� is the vector potential of the xuv light in thedipole approximation and thus omitting the spatial depen-dence eikr. To calculate the laser-assisted version of this pro-cess, the plane wave in the final state is replaced by a Volkovwave �V of the same momentum p as follows:

�S − 1� fi = − i−�

�

dt��V�AX�t� · p� 0 . �4�

In this approach, the influence of the ir field A on the initialstate, as well as the influence of the sample potential V on thefinal continuum state, are neglected. The former is justifiedeven for weakly bound systems as long as V is a short-rangepotential �27�, while the latter holds in the soft photon limit.From these two S-matrix elements, the ratio of the laser-assisted and the field-free photoemission cross sections canbe derived �29� as follows:

An =d��n�/d�

d�/d�= Jn

2�p · E0

�ir2 ,

Up

2�ir� � Jn

2�p · E0

�ir2 � . �5�

In the approximation of Eq. �5�, the ponderomotive potentialis neglected. As is the case in the soft photon limit, the targetatom properties cancel and the sideband amplitude dependsonly on the electron and ir light properties. It is thereforeexpected that, to the extent that the soft photon approxima-tion is justified, target properties are negligible.

III. ASPECTS OF SURFACE LAPE

In principle, the concept of the laser-assisted photoelectriceffect should also apply to solid surfaces, and should resultin the convolution of sideband shifts onto the entire continu-ous xuv photoemission spectrum from the solid. However,due to the manifold different excitation paths and energydissipation channels, the interpretation of energy shifts in thephotoemission spectra from solid surfaces is more compli-cated than in the gas phase. In the following we discusspossible influences of the strong ir light on the photoemis-sion spectra from solids.

A. Momentum conservation and ground state dispersion

A basic difference between photoemission from crystalsurfaces, when compared to photoemission from atoms, con-cerns the exchange of momentum. This is restricted to inte-ger multiples of the reciprocal lattice vector �G in a crystal,due to the periodicity of the lattice. However, the presence ofa surface removes the periodicity in one half-space and soft-ens momentum conservation. In the case of xuv photoemis-sion, the electrons have a very short escape depth of theorder of 5 Å, according to the universal curve �30,31�. They

ω IR

ωXUV

E=0

ground state

con

tin

uu

m

FIG. 1. The principle behind the laser-assisted photoemissionprocess for atoms in the “soft photon” limit. LAPE is described intwo steps. First, the ground state electron is photoemitted into anexcited state in the continuum by the xuv pulse, neglecting theinfluence of the ir field. Then the photoemitted electron evolves as afree electron in the ir field, unaffected by the atomic potential. Thisresults in a redistribution of the electrons in the continuum by ab-sorption and stimulated emission of ir photons.

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thus sense only one or two atomic layers. The surface canthen act as a continuous source or sink of momentum normalto the surface �32�, and the electron can be excited into asurface state, often called the inverse low energy electrondiffraction �LEED� state. Along the surface normal, the latteris essentially a plane wave. For an ir laser pulse impingingon a metal surface, the electric field components parallel tothe surface nearly vanish because of the boundary condi-tions. The remaining field, i.e., the component that is able todress the photoemitted electrons, thus points along the sur-face normal, where the surface can balance momentum con-servation. In this direction, the interaction of the emittedelectron with the ir laser can be described by replacing theplane wave part of the LEED final state by a Volkov wave.

However, in xuv photoemission, part of the spectrumarises from direct transitions, e.g., the emission from d bandsinto s bands in transition metals. This photoemission processconserves the momentum q� parallel to the surface. As the“dressing” is associated with a momentum change along thesurface normal, the direction of emission of the electron is ingeneral changed, except for electrons emitted normal to thesurface. For angle-resolved photoemission spectroscopy withinfinite resolution, this means that in laser-assisted photo-emission, the detected sidebands stem from electrons emittedfrom different initial states and at slightly different anglescompared with the electrons that did not lose or gain photonsof energy �� from the ir field. Due to the dispersion of thevalence bands in solids, the corresponding energies can beshifted leading to a deviation of the sideband energy spacingcompared with the ir photon energy. However, in the softphoton limit, the relative momentum change associated withthe exchange of a photon between the photoelectron and their field is small. At an observation angle of 45°, the absorp-tion or emission of a 1.6 eV photon by a 36 eV electronleads to �k� =0.05 Å−1, which is about 0.02 of the total Bril-louin zone. The corresponding energy shift due to dispersionis at most 50 meV, which is significantly smaller than the irphoton energy �1.59 eV� and even below the energy reso-lution of our detector. Thus, we neglect these dispersion en-ergy shifts in this work.

B. Resonant interband and intraband transitions

Another difference between atoms and surfaces is thequasifree behavior of electrons in a band, due to the delocal-ization of the electrons from individual ions. At the Fermiedge of Pt however, the energy spectrum is dominated by dbands, which deviate significantly from the free-electron-likesp bands. Due to the strong localization of the d electrons tothe crystal ions, the d bands are narrow and exhibit only lowdispersion. They can be described in the tight-binding ap-proximation and resemble bound electrons in atoms �33�.Ground state dressing of the d electrons is therefore ne-glected in the soft photon limit for the same reasons as inatoms �34�. For the broader sp bands, the tight-binding ap-proximation does not hold. However, although the electronscan move freely, they cannot respond to the ir light in thesame way as electrons in the continuum. At low frequencies,the interaction of light with a metal is dominated by intra-

band absorption. In this process, which corresponds to theclassical ir absorption picture, electrons can absorb any pho-ton energy from the ir field and are promoted into unoccu-pied levels above the Fermi edge. This mechanism thus onlyaffects a small fraction of the electrons, in a narrow windowaround the Fermi edge, and does not lead to sideband peaks.Moreover, resonant k�-conserving interband transitions areonly possible in certain directions when energy and momen-tum conservation are fulfilled. Contrary to the case of con-tinuum electrons, only absorption is possible from theground state, because stimulated emission is forbidden by thePauli principle as the lower lying states are filled. The pres-ence of such resonant interband transitions should thus bevisible by an enhancement of the positive sideband; i.e.,conduction-band electrons can absorb photons from the laserfield. The dependence of this contribution on the ir-xuv timedelay should follow the lifetime of the intermediate states,which is of the order 100 fs for transition metals �35�. Botheffects are not observed in our experiment.

C. Nonresonant interband transitions

Due to the high ir intensities applied in LAPE experi-ments, nonresonant ir interband transitions into virtual levelsoccur which can serve as intermediate states for multiphotonionization. Such transitions have been studied theoreticallyin atoms in different limiting cases. For electrons in excitedRydberg states of atoms, nonresonant absorption and emis-sion of microwave photons into virtual states can lead todressing analogous to the continuum �36�. As unoccupiedreal levels above and below the initial Rydberg state aredensely spaced, both absorption and emission are equallylikely, which leads to symmetric sidebands. For electrons inan atomic ground state, symmetric sidebands can occur whenthe photon energy of the dressing beam is considerablysmaller than the spacing between the atomic levels. In thiscase, which is usually fulfilled only for light in the far ir ormicrowave region, the distance of the virtual states after ab-sorption and emission are approximately equally spacedfrom the closest unoccupied level �37�.

In our experiment, the electrons are in the ground stateand the photon energy is not resonant with an interband tran-sition. Nonresonant absorption is closer to resonance with anunoccupied real state than stimulated emission, since unoc-cupied levels are only available above the ground state.Dressing of the ground state is thus expected to preferentiallyenhance the positive sideband leading to asymmetric ampli-tudes. In the light-metal interaction volume, however, theelectron number reaches the same order of magnitude as thenumber of photons per pulse applied in our experiment. As aconsequence, only a very small fraction of the electrons isexcited into the virtual states, leading only to a negligiblecontribution to the positive sideband in the xuv photoemis-sion spectrum. This is in contrast to gaseous atoms where theatom density is usually much lower than the photon density.In the case of dressing of the final state, only the small num-ber of photoemitted electrons plays a role—so that in thecontinuum, a significant fraction of the electrons can bedressed.

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D. Dressed band structure

Theoretical investigations of intense field effects in solidspredict the opening of band gaps �38,39� whenever directmultiphoton transitions are possible. These band gaps areclosely related to the intensity-dependent Autler-Townessplitting �40� of atomic levels in the presence of a resonant ornear-resonant strong laser beam. At a photon energy of1.6 eV, the laser is not resonant with any direct interbandtransition �41�, so that ground state dressing is expected toplay a minor role in our experiment. The strong ir laser thusinfluences the electrons only after photoemission, leading tothe final state dressing picture similar to the experimentsdone in gaseous atoms.

E. Competing strong-field effects

For applications of LAPE in xuv pulse duration measure-ments, the sideband amplitude range, after Eq. �5� An=Jn

2�x� for small values of the argument x is of special inter-est. In système international ď unités �SI� units x can bewritten as

x =�16��

me�

IEkin

�ir4 . �6�

For small x, A1 can be approximated by A1�x2 /4 leading to

A1 �IEkin

�ir4 . �7�

In this regime, the sideband height depends linearly on the irlaser intensity, which makes it a suitable observable forxuv-ir cross-correlation measurements as well as for time-resolved spectroscopy. Additionally, A1 depends on the ki-netic energy Ekin of the dressed electron and on the ir photonenergy �ir. Figure 2 shows the intensity required to generatefirst-order sideband amplitudes of A1=0.1 versus the photo-electrons’ kinetic energies Ekin for 800 nm light. For kineticenergies below 100 eV, an intensity of at least 1011 mW /cm2

is necessary. For slower electrons, the required intensity in-creases dramatically. This intensity range is only one to two

orders of magnitude below the damage threshold of metalsurfaces. Also, the excitation of nonthermal hot electronsleads to changes in the spectra similar to those caused by thephotoelectric effect. Finally, the illumination of metal sur-faces at such high intensities leads to significantly strongerelectron emission and higher kinetic energies than from gas-eous atoms, due to field enhancement and space-charge-induced Coulomb explosion.

In past work, it was shown that above-threshold photo-emission �ATP� can be significant from surfaces at muchlower laser intensities than in atoms due to field enhance-ment effects �42�. Above-threshold photoemission is the pho-toemission of electrons from a surface by absorption of morephotons than is required to overcome the work function. Thiseffect can be understood, similar to LAPE, by the rate-limiting multiphoton ionization of the sample by absorptionof the minimum number of photons needed, and followed byredistribution of these electrons in the continuum by ab-sorption of additional photons �28�. For ultrashort Ti:sap-phire laser pulses at 780 nm, intensities of the order of1014 W /cm2 are needed to cause a substantial emission ofelectrons by multiphoton ionization of gaseous atoms; i.e.,above-threshold ionization. However, it has been known fora long time that surface plasmons can lead to substantial fieldenhancement �up to a factor of 103� corresponding to inten-sity enhancements of 106 on a metal surface. This effectresults in phenomena such as surface-enhanced Raman scat-tering. Although forbidden by energy and momentum conser-vation on perfectly flat surfaces, these surface plasmons canbe excited on rough surfaces. Due to the corresponding fieldenhancement, ATP can happen at intensities as low as108 W /cm2 �42�. These enhancements not only lead tohigher kinetic energies of the ATP electrons than thecorresponding above threshold ionization �ATI� from atoms,but furthermore the number of electrons is considerablylarger. Additionally, the first step in ATP—multiphotonionization—is stronger than in atoms, because of the lowionization potential �work function� of solids. Finally, thesample particle density is higher than in typical experimentson atoms. As a consequence, many electrons can be emittedfrom a very small volume of the solid sample by a singleintense laser pulse. This leads to a Coulomb explosion as theelectrons repel each other �43,6�. This way some of the elec-trons are accelerated and can gain a significant amount ofextra kinetic energy, while others are decelerated and maynot escape the surface. Surface preparation thus plays a ma-jor role in the ability to successfully observe LAPE.

The purpose of this work is to extract from ir-xuv photo-emission data unambiguous signatures of all the processesthat occur when a surface is illuminated simultaneously withan xuv and intense ir fields, i.e., ATP, heating of the valenceelectron distribution, and LAPE. Comparing the relativemagnitudes of these effects allows us to develop methods tounambiguously single out the continuum free-free transitionscorresponding to LAPE. We find that LAPE is the dominantprocess over a wide range of ir intensities and polarizationstypically employed in experiments investigating chargetransfer dynamics in surfaces and surface-adsorbate systems.This result shows the feasibility of extending the variety oftime-resolved measurements using LAPE that have been ob-

1010

1011

1012

1013

Inte

nsity

(W/c

m2 )

1009080706050403020100electron energy (eV)

800 nm1600 nm

FIG. 2. Calculated ir intensity required to generate first-ordersideband heights of A1=0.1 for wavelengths of 800 and 1600 nm,respectively, as a function of the kinetic energy of the electrons. Forkinetic electron energies of 36 eV and an 800 nm dressing wave-length, laser intensities greater than 1011 W /cm2 are required.

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served and employed in atomic and molecular samples, tosolid surfaces.

IV. EXPERIMENTAL SETUP

Figure 3 shows the experimental setup. A temperature-controlled Pt�111� sample is mounted on a translation androtation stage inside an ultrahigh vacuum �uhv� chamber. Toavoid quenching of the peaklike d-band structure at theFermi edge by adsorption of contaminants, the sample iscleaned at regular intervals using three cycles of annealingwith oxygen at 920 K and flashing to 1300 K. At the basepressure of 3�10−10 mbar, the Pt surface stays clean forseveral hours. For the measurements, the sample was cooledto 84 K using liquid nitrogen.

A Ti:sapphire multipass amplifier laser system producing1.5 mJ, 780 nm pulses at a repetition rate of 2 kHz, and witha duration of 25 fs is used to generate the ir and xuv beams�44�. Approximately 30% of the laser energy is used for their dressing beam, while the remaining 70% are upconvertedby phase-matched high-harmonic generation in an argon-filled hollow waveguide �45�. A pair of Si:Mo multilayermirrors—one flat and one curved—is used to spectrally se-lect the 27th harmonic �at a wavelength of 30 nm, corre-sponding to a photon energy of 42 eV� and to focus this xuvbeam onto the Pt surface in a beam with a spot size of theorder of 100 �m. Additionally, an aluminum filter of 200 nmthickness is used to maintain a pressure differential betweenthe high-order harmonic generation �HHG� cell and the uhvchamber, and to block the copropagating ir light while trans-mitting the xuv beam. As shown in Fig. 4, the xuv beam,containing about 106 photons per pulse after these opticalelements, irradiates the sample at a variable angle � withrespect to the surface normal. The kinetic energies of thephotoemitted electrons are analyzed at 90° with respect tothe incoming xuv beam, using a 600-mm-long time-of-flight

detector �TOF�. Its angular acceptance is �2°, correspondingto a solid angle of 3�10−4 steradians. In order to preventlight reflected off the sample hitting the detector, the TOFtube is tilted up with respect to the plane of incidenceby an angle of 20°. Consequently the observation angle �with respect to the surface normal is given by cos �=cos 20° cos�90−��.

The ir beam is directed onto the surface through a variableoptical delay stage and focusing lens, and overlaps with thexuv beam on the sample at a small �1° � angle. Its pulseduration is broadened to �35–40 fs by dispersion as itpropagates through various optical elements in the delay line.The maximum ir power available is 300 mW, and the beamspot size is varied between 0.4 and 1.2 mm by moving thefocusing lens. The ir beam is chopped at 1 kHz, and the TOFdetector is gated to record ir-xuv and xuv-only spectra alter-nately. This allows us to distinguish between emissioncaused solely by the ir beam �such as above-threshold pho-toemission� from two-color �ir-xuv� photoemission. More-over, the availability of both ir-xuv and xuv-only spectramakes it possible to unambiguously observe the laser-induced free-free transitions in the continuum, as will bediscussed further below.

The spatial and temporal overlap between the ir and thexuv beams at the sample is obtained using a multistep pro-cedure. A preliminary spatial overlap is obtained by movingthe sample holder so that the two beams hit a phosphorscreen that is moved in place of the Pt�111� surface. Thebeams are observed and aligned using a charge-coupled de-vice �CCD� camera that images the phosphor from outsidethe chamber. The temporal overlap is obtained by moving thesample holder to another position, where the beams passthrough a BBO frequency-doubling crystal. The aluminumfilter in the xuv beamline is replaced by a thin �0.355 mm�sapphire window to allow the ir light from the high-harmonicxuv beamline into the uhv chamber. A cross correlation be-tween the two ir fields then locates time zero. The position oftime zero must be corrected for the sapphire window groupdelay, which is 934 fs. At this point, the Pt�111� sample ismoved into place. Since the position of the phosphor screenalong the light direction is not exactly the same as thePt�111� sample, the spatial overlap must be readjusted. Thisis done using LAPE itself, by observing the highest-energy

Ti:Sapphire amplifier system

25 fs, 2 kHz, 1.5 mJ/pulse

UHV

TOF

e−

Argon

glass capillary

delay stage

Al filter

chopper

pumpmultilayer mirrors

pump

BS

FIG. 3. Experimental setup for observing the laser-assisted pho-toelectric effect from surfaces. ir pulses from a Ti:sapphire laseramplifier are split into two. One beam is directed onto the surfacethrough a variable optical delay stage and an optical chopper run-ning at half the repetition rate of the laser. The other beam is up-converted into the xuv regime using phase-matched HHG in anArgon-filled glass capillary. Two multilayer mirrors select the 27thharmonic at 30 nm /42 eV and focus it onto the Pt�111� sampleinside a uhv chamber. The crystal is mounted on a rotation stageand cooled to liquid nitrogen temperature. A TOF detector measuresthe kinetic energies of the photoelectrons emerging from thesample.

surface normal

laser beam

p-polarization

TOF

θϕ

20° Pt sample

FIG. 4. Geometry for the LAPE measurements: p-polarized irlight impinges on the Pt sample at an angle � with respect to thesurface normal. �=90−� is the angle of the polarization vectorwith respect to the surface normal. The detector is tilted by 20° withrespect to the plane of incidence. The corresponding observationangle � with respect to the surface normal is given by cos �=cos 20° cos �.

SAATHOFF et al. PHYSICAL REVIEW A 77, 022903 �2008�

022903-6

photoelectrons as a measure of spatial and temporal overlap.

A. Above-threshold photoemission

As has been discussed above, the ir laser intensity at800 nm required to generate sidebands is of the order of1011 W /cm2. Since the parallel component of the electricfield nearly vanishes at the surface of a good conductor, thelaser polarization must be perpendicular to the surface. Fig-ure 5 shows a photoemission spectrum taken for p-polarizedir light as the laser intensity is varied around 1011 W /cm2.No xuv light was incident in this measurement. Since theponderomotive potential at these intensities is �0.1 eV andis much less than the work function of Pt �5.8 eV�, no“channel-closing” occurs, and at least 4 ir photons are re-quired to photoeject electrons from the surface. The lowestintensity curve basically shows multiphoton photoemissionby four photons, with a small contribution of above-threshold photoemission by five photons. As the intensity isincreased, two effects can be observed. First, above-threshold photoemission becomes stronger. The five-photonedge increases and new channels with six and seven photonsappear. However, at higher laser intensities the separations ofsubsequent edges are measurably larger than the ir photonenergy. This is due to the fact that the number of photoelec-trons increases dramatically and leads to a Coulomb explo-sion of the electron cloud due to their mutual repulsion �6�.As a result, faster electrons at the front of the cloud areaccelerated, while slower electrons at the back are deceler-ated. This effect already becomes very strong at the moderatelaser intensities applied here. In contrast to experiments ongaseous samples, the higher target densities and lower ion-ization potentials in solids lead to stronger multiphoton ion-ization, above-threshold photoemission, and as a conse-quence, also to stronger space-charge acceleration. To detectLAPE from solids with Ti:sapphire laser pulses at 800 nm,xuv photon energies of at least 30–40 eV are required so thatthe photoejected electrons corresponding to the Fermi edgehave energy significantly higher than the IR-induced ATPelectrons. However, even if the xuv photoelectron Fermiedge lies beyond the high-energy ATP electrons, its shapecan still be altered by the space charge if too many ir-inducedelectrons are emitted. It is therefore important to reducespace-charge effects as much as possible.

The measurement shown here was performed on a samplethat was cleaned as described above. This is necessary sinceany surface roughness can lead to strong local enhancementsof the ir field at the surface �42� which dramatically increasesthe number and energy of ir-ejected electrons. Due to thestrong susceptibility of these effects to surface roughness, their-induced electron spectra differ strongly from day to day,and Fig. 4 can thus only be taken as an example. We observethe creation of hot spots on the Pt�111� surface resultingfrom ir laser intensities above �1012 W /cm2 at pulse dura-tion �30 fs. These hot spots result in a huge increase inhigh-energy electrons resulting from the ir field. Apart fromusing shorter pulse durations to raise this damage threshold,the use of lower ir photon energy as the dressing field wouldhelp to circumvent this problem. Due to the �ir

−4 dependence

of the sideband amplitudes in Eq. �7�, increasing the wave-length of the ir by a factor of 2 would reduce the intensityrequired to generate sidebands by a factor of 16. High-poweroptical parametric amplifiers �46� would thus facilitate LAPEexperiments on metal surfaces. In the present experimenthowever, ir-induced electrons can be kept sufficiently low bythorough sample preparation and by restricting the ir laserintensity to moderate values.

B. Extraction of the sideband structure

As mentioned before, LAPE has been extensively studiedin the gas phase, where the discrete nature of the photoelec-tron spectrum makes the sidebands easy to distinguish. Toextract this peaklike sideband structure from the continuousspectra of solid surfaces, the ir-xuv spectrum must be decon-volved from the xuv-only spectrum using a fitting procedure.Figure 6 shows a series of photoelectron spectra around theFermi edge, at an ir peak intensity of the order of1011 W /cm2 and for relative time delays between the ir andxuv beams ranging from −100 fs to +100 fs. Negative timedelays mean that the ir pulse comes after the xuv pulse. Their beam was polarized in the plane of incidence �p polarized�.The xuv-only spectrum is only shown for the −100 fs mea-surement �dashed line�. At this time delay, both the xuv-only,as well as the ir-xuv spectra, show the typical d-band struc-ture of clean Pt�111�. This Pt d-band peak near the Fermiedge, although 0.9 eV wide, is nevertheless a very usefulcharacteristic peak around which to observe sidebands.While the spectral shape is unaffected by the presence of their field, the ir-xuv spectrum is slightly shifted to higher elec-tron energies as compared to the xuv-only spectrum due tothe space-charge-induced Coulomb explosion. We have ob-served this space-charge-induced shift to be present for timedelays between at least −1 ps and +1 ps. This can be ex-plained by the fact that the photoemitted electrons are trav-eling slowly enough that they do not escape from the rangeof the space-charge field of the ir-induced electron cloudduring the time frame of the experiment. Thus, the xuv pho-toelectron energies are slightly shifted even when the ir pulsecomes considerably after the xuv. This space-charge effect

� ��

� ��

� ��

� ��

� ��

� ��

���

� �� �� �� �� ���

� � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � ��

� � �� � � � � � � � � � � � � � �� � � � � ! � � � � � � � �� �

FIG. 5. �Color online� Photoemission spectra taken at differentlaser intensities ranging from 130 to 590 mW /cm2 using ir lightonly. ATP �above-threshold photoemission� and space-charge accel-eration generate electrons with kinetic energies of tens of eV.

LASER-ASSISTED PHOTOEMISSION FROM SURFACES PHYSICAL REVIEW A 77, 022903 �2008�

022903-7

increases strongly with the ir intensity. At very high intensi-ties it not only shifts the ir-xuv spectra but also changes itsshape �see, e.g., Fig. 16�. However, in Fig. 6, the space-charge effect is rather low, indicating an effective ir intensityin the low 1011 W /cm2 range. The space-charge shift is de-termined from the −100 fs curves and all ir-xuv spectra arecorrected for it before subsequent analysis.

In the photoemission spectrum shown in Fig. 6 near thatwhich corresponds to zero time delay between the laser andxuv pulses, we observe a very strong shape change at theFermi edge. Insight into the origin of this change can begained by calculating the average kinetic energy of the pho-toelectrons above 20 eV, both with and without the ir pulsepresent. �Below 20 eV photoelectron kinetic energies, the ir-xuv spectrum is dominated by low-energy electrons fromabove-threshold photoemission.� No significant ir-inducedincrease of the average kinetic energy was found around zerofs. Indeed, the calculated average photoelectron kinetic ener-gies with and without the ir were identical, within 0.1 meV,at all time delays. This indicates an essentially equal redis-tribution of electrons to lower and to higher kinetic energiesin the presence of the ir field that modifies the photoelectronspectra. This result therefore excludes interpretations of aphotoelectron spectrum modified by image potential states,ground state dressing, or hot electrons, �47� since in all cases,the average kinetic energy should be increased by the pres-ence of the ir field. We therefore interpret the Fermi edgemodification near time zero to be the result of the laser-

assisted photoelectric effect. Viewed in a perturbative two-step model, the electrons photoemitted by the xuv beam canabsorb or emit photons from the ir field, leading to sidebandsin the photoelectron spectrum. In an atomic system, the xuvphotoelectron spectrum consists of discrete atomic peaks,and the LAPE sidebands are easily distinguished. From asurface, the photoemission spectrum consists of a continuousdistribution due to the band structure of the solid. Neverthe-less, the high density of states at the Fermi edge for Pt�111�does allow one to discern sideband peaks at �1.6 eV.

To quantitatively extract the sideband intensities in thecase of photoemission from Pt in the presence of an intenseir field, we modeled the absorption and emission of up to twoir photons by a photoelectron of kinetic energy E0 by

f�E − E0� =1 − 2A1 − 2A2

�2��2e�E − E0�2/2�2

+ �� A1

�2��2e�E − E0 � ���2/2�2

+A2

�2��2e�E − E0 � 2���2/2�2� �8�

�see Fig. 7�. Since the kinetic energies of the affected elec-trons are large compared to the ir photon energy �soft photonlimit�, we assume that the influence of the ground state onthe free-free transitions is negligible. In particular, the aboveLAPE response function is considered independent of theelectron’s kinetic energy over the fit range around the Fermiedge. Consequently, the ir-xuv spectrum is expected to begenerated by a convolution of the xuv-only spectrum with aLAPE response function of Eq. �8�. We therefore fit thisconvolution to the combined ir-xuv photoemission spectrum,allowing the sideband intensities A1 and A2, as well as thewidth � and the peak separation ��, to be fit parameters. Thefactor in front of the first Gaussian peak is chosen to normal-ize the response function to 1. The parameters A1 and A2 thusgive the fraction of electrons scattered into the first and sec-ond sidebands, respectively. Figure 8 shows the result forzero time delay between the ir and xuv beams. The dottedline gives the photoemission spectrum without the ir pulsepresent. The solid line shows the photoemission spectrumwith the ir pulse present. Finally, the dashed line shows the

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40353025electron energy (eV)

Time Delay (fs)

100

80

60

40

20

0

- 20

- 40

- 60

- 80

-100

FIG. 6. Observed photoelectron spectra from Pt�111� as a func-tion of time delay between the ir and xuv beams. For −100 fs timedelays, the xuv-only spectrum �dashed line� is also shown. A slightshift of the spectrum due to ir-induced space charge can be seen, butthis does not change the shape of the spectrum and can thus becorrected for. The strong modification at the Fermi edge of the timezero spectrum is due to laser-assisted photoemission.

1.0

0.8

0.6

0.4

0.2

0.0

LAP

Ere

spon

se

-4 -2 0 2 4E-E0 (eV)

without irwith ir

FIG. 7. Calculated LAPE response function using Eq. �8�assuming the generation of two sidebands.

SAATHOFF et al. PHYSICAL REVIEW A 77, 022903 �2008�

022903-8

fit to the ir-xuv curve by convolving the LAPE responsefunction from Eq. �8� with the unperturbed spectrum. Theinset of Fig. 8 shows the LAPE response function associatedwiththe resulting fit parameters: A1=0.241�0.004, A2=0.013�0.003, �=0.23�0.02 eV, and ��=1.59�0.02 eV. It ismultiplied by �2��2, so that the peak heights reflect thecorresponding intensity parameters A1 and A2.

The fit to the sideband separation of ��=1.59 eV corre-sponds very well to the photon energy of the ir beam, whilethe width � reflects closely the convolution of the laser band-width ��0.1 eV� and the detector resolution at the high-energy part of the photoelectron spectrum ��0.2 eV�. Ini-tially, we allowed the response function to be asymmetricusing different intensity parameters A1,2

� for the positive andnegative sidebands. However, this fit generally yielded side-band heights that were identical for the high- and low-energysidebands, as would be expected for the LAPE in this weak-field regime �see Fig. 9�. The quality of the resulting fitstrongly supports the interpretation of these data as surfaceLAPE. This is further corroborated by the fact that no side-

bands are observed when the polarization of the ir light isperpendicular to the direction of detection �s polarized, seeFig. 18�a��. However, hot electrons can be observed for bothpolarizations of the ir field. These hot electron-energy distri-butions persist for significantly longer times than the LAPEresponse �hundreds of femtoseconds�, and are discussedbelow.

By fitting the photoelectron spectra for all other time de-lays, with �� and � fixed to the values derived from the timezero photoemission spectrum, we determine the strengths A1of the first-order sideband as a function of delay between their and xuv pulses �Fig. 10�b��. The small error bars show thelarge sensitivity of the fit to the sideband heights, which isdue to the fact that the positive sidebands show up in a re-gion well beyond the Fermi edge, where the xuv-only spec-trum only exhibits a small count rate. For a cross-correlationmeasurement, an observable which is linear in the laser in-tensity IL is required. As shown in Fig. 10�a�, A1 fulfills thisrequirement for small IL, where A1 is approximated by theasymptote A

1*=x2 /4, and, following Eq. �6�, x2� IL. For

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√⎯⎯ 2π

σf(

E-E

0)

-4 0 4E-E0 (eV)IR-XUV

XUV onlyfit

FIG. 8. Photoemission spectrum at zero time delay between their and xuv fields, taken from the data shown in Fig. 6. Observedphotoemission spectrum with �solid line� and without �dotted line�the ir pulse present. The dashed line shows the fit to the ir-xuv curveby convolving the LAPE response function from Eq. �8� with theunperturbed spectrum. The inset shows the LAPE response functionassociated with the fit.

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4540353025electron energy (eV)

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σf(

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-4 0 4E-E0 (eV)

IR-XUVXUV onlyfit

FIG. 9. Identical spectrum to that shown in Fig. 8, where thepositive and negative first-order sideband heights are allowed tovary separately during the fit. However, no significant asymmetry isgenerated as a result of this fit.

0.4

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0.0sidebandheightA1,A

1*

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A1

A1*fit

a)

b)

0.8

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0.4

0.2

0.0

A1,A1*

3.02.52.01.51.00.50.0x2

A1 = J12(x)

A1* = x2/4

FIG. 10. �a� The solid line shows the square of the Bessel func-tion A1=J1

2�x�, plotted versus x2� I. The dotted line depicts the as-ymptote behavior for small x: A

1*=x2 /4. For a cross-correlation

measurement, a linear intensity dependence of A1 is required, whichis only fulfilled for small x. �b� Measured cross correlation of the ir�of duration around 35 fs� and the expected �10 fs duration xuvpulses as a function of time delay. The measured sideband heightsA1 are replaced by the corresponding values A

1* of the asymptote, so

that linear intensity dependence is ensured for all data points. AGaussian fit yields 33�2 fs, limited by the duration of the ir pulseduration. A Gaussian fit to the uncorrected A1 data yields 37�3 fs.

LASER-ASSISTED PHOTOEMISSION FROM SURFACES PHYSICAL REVIEW A 77, 022903 �2008�

022903-9

larger intensities, however, A1 levels off and exhibits a sub-linear behavior. To ensure a linear dependence for all datapoints, the sideband heights A1 are thus replaced by the cor-responding values A

1* of the asymptote. A Gaussian fit yields

a full width at half maximum of 33�2 fs, in accordancewith the expected xuv pulse duration of �10 fs and the irpulse duration of the order of 35 fs, respectively.

Figure 11 shows a LAPE measurement at an angle ofabout �=5° between the ir polarization �p polarized� and thesurface normal, close to grazing incidence. At this sampleangle, which corresponds to an observation angle of about20° with respect to the surface normal, the d-band peak at theFermi edge is even more pronounced than in the previousgeometry, and it dominates the broader d-band structure at30 eV. As a result, the sideband characteristics of the LAPEprocess become even more obvious. The steps due to thefirst- and second-order positive sidebands are more pro-nounced and the first-order negative sideband is visible.Moreover, like in the previous data set, the ir-xuv spectrumcan again be reproduced from the xuv-only data by convo-lution with the symmetric sideband function of Eq. �8�. Thisresult has been found at several other sample angles as well,which are not shown here. The universal applicability of thisfit procedure to data taken at different sample angles ex-cludes band structure effects, e.g., the opening of band gaps�38,39�, to be the cause for the observed ir-induced modifi-cations to the photoemission spectra.

Figure 12 shows a time series of LAPE spectra �solid graycurves� between −40 fs and 40 fs in steps of 5 fs, taken atthe new geometry ��=5° �. The dotted curves represent thexuv-only spectra and the dashed curves are the fits. In thisdata set, the space charge turns out to be stronger than in theprevious measurement. This may be due to higher surfaceroughness, which depends on the cleaning procedure andthus changes from day to day. The corresponding shift tohigher energies of the ir-xuv spectra with respect to the xuv-only curve is already corrected for in Fig. 12. In addition, thedata at −40 fs �where the ir pulse comes after the xuv pulse�reveal a slight smearing of the ir-xuv spectrum, caused bythe space-charge-induced Coulomb explosion. Despite thissmearing, the fit procedure still qualitatively reproduces their-xuv spectra, especially the steplike structure in the spectrathat show strong LAPE. Quantitatively however, the space-

charge distortion will lead to systematic deviations of the fitparameters A1 and A2. These sideband heights are plottedversus time delay in Fig. 13. A1 grossly follows the expectedGaussian cross-correlation characteristics as in the previousdata set. However, it does not go to zero at the wings mainlybecause of the space-charge effects. Moreover, the back-ground is not constant, but is higher for positive time delays.This background is most likely composed of a constant partdue to the space-charge effect and, above time zero, a time-dependent part from hot electrons. We will discuss these ef-fects in more detail in the following sections of this paper,but will not take it into account in the discussion of the

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4240383634323028electron energy (eV)

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√⎯⎯ 2π

σf(

E-E

0)

-4 -2 0 2 4E-E0 (eV)IR-XUV

XUV-onlyfit

FIG. 11. LAPE spectrum taken at a different sample angle of 5°.Due to the larger d-band peak at this angle, the negative sideband ismore clearly visible.

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0

- 5- 10

- 15

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- 35

- 40

IR-XUVXUV-onlyfit

FIG. 12. LAPE time series for ir-xuv pulse separations between−40 fs and 40 fs in steps of 5 fs. The dotted lines show the xuv-only data. The ir-xuv spectra �solid gray lines� are corrected for a0.1 eV space-charge shift. The dashed lines show the symmetricfits.

0.25

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eban

dIn

tens

ities

A1,

2

-40 -20 0 20 40Time Delay (fs)

A1

A2

fit

FIG. 13. Amplitude of the first-order �circles� and second-order�squares� sideband intensity versus time delay. The fits result inFWHM of 37�5 fs and 35�3 fs for the first- and second-ordersidebands, respectively.

SAATHOFF et al. PHYSICAL REVIEW A 77, 022903 �2008�

022903-10

present data set. A tentative Gaussian fit of the A1 curve inFig. 13 yields a width of 38�5 fs, similar to the previousmeasurement.

Due to the larger number of data points, the present timeseries makes it possible to investigate the time dependence ofthe smaller second-order sideband height A2 �see Fig. 13�. Itfollows a similar Gaussian curve with a width of 35�3 fs, inagreement with the time dependence expected from the pulselengths. Moreover, despite the contributions from hot elec-trons and space charge, we can perform a coarse check ofEq. �5� by comparing the maxima of A1 and A2. For theobserved A1

max=0.25�0.02 we expect, after An=Jn2�x�, an ac-

companying A2max=0.026�0.06, which agrees reasonably

with the measured value of 0.038�0.002.Figure 14 shows an alternative analysis of the data using

the d-band peak at the Fermi edge. After subtraction of thexuv-only curves in Fig. 12 from the xuv-ir data, two maximaarise around 34 and 37 eV, originating from the first- andsecond-order sideband, respectively. Additionally, the deple-tion of the d-band peak leads to a minimum in the subtracteddata. These three extrema are plotted versus time delay inFig. 14. Gaussian fits result in widths of 36�4 fs for thepositive sideband, 37�6 fs for the negative sideband, and38�5 fs for the zeroth order, which agree with each otherand with the pulse widths within their error margins. In sum-mary, dressing of pronounced peaklike structures in the elec-tron spectra of solids can be detected by a direct comparisonof the xuv-only and the ir-xuv data and by monitoring thesideband heights or, more sensitively, by the depletion of thephotoemission peak. Alternatively, if the structure is morecomplicated, the convolution of the xuv-only data with asideband function has to fit to the ir-xuv data. In any case,the dressing makes it possible to, in principle, measure thetime when electrons are ejected from surfaces or adsorbatesby photoemission or subsequent Auger decay. To achieveoptimum time resolution, other ir-induced effects such asspace-charge acceleration or hot electron excitation must beminimized. One promising route to this goal is the use oflonger wavelength ir light. Following Eq. �7�, the requiredlaser intensity to generate sidebands of a certain height isproportional to �ir

4. Figure 2 shows the intensity to generate

A1=0.1 for a wavelength of 1600 nm, which could bereached by a high-intensity optical-parametric amplifier �46�.Compared to 800 nm, as used in this work, 16 times lessintensity is needed. This would diminish most other effectsdramatically.

As scattering of photoemitted electrons within the mate-rial leads to large angle and energy changes, scattered elec-trons are effectively removed from the part of the spectrumnear the Fermi edge that we analyze. The observed electronsthus essentially originate from a thin layer defined by their�5 Å mean free path. We believe that the finite transit timethrough this layer ultimately limits the resolution of surfaceLAPE for characterizing xuv pulses or for measuring ul-trafast inner-shell electron dynamics in solids. In our case,this value is �200 attoseconds, and thus does not limit ourmeasurement. Still higher resolution could be obtained byincreasing the xuv photon energy, and thus the emitted pho-toelectron energies, so that they escape more quickly. There-fore, this result also opens up new possibilities for studyingfemtosecond-to-attosecond correlated electron dynamics insolids.

C. Laser intensity dependence of LAPE from surfaces

To study the intensity dependence of the first-order side-bands, we first investigated the influence of the sample onthe effective intensity on the surface. To this end, the ir lightwas p polarized and the surface was rotated horizontally tothree different angles � between the ir polarization and thesurface normal. �=0° denotes grazing incidence with thepolarization being perpendicular to the surface. �=90° de-notes normal incidence and parallel polarization with respectto the surface. Figure 15 shows the amplitude A1 of the first-order sideband extracted at three different angles. Towards�=90°, A1 decreases strongly. This sample angle depen-dence can be fit with a cos2 consistent with the assumptionthat only the electric field exactly at the surface interacts with

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side

band

inte

nsity

(a.u

.)

-40 -20 0 20 40Time Delay (fs)

positive sidebandnegative sidebandcarrier

FIG. 14. Positive and negative sideband heights �upper curve�and depletion of the d-band peak �lower curve� versus time delay.The Gaussian fits �solid lines� yield 36�4 fs for the positive side-band, 37�6 fs for the negative sideband, and 38�5 fs for thedepletion signal, respectively.

laser beamp-polarized

TOF

0.25

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0.00

sidebandheight

A1

100806040200sample angleϑ (degrees)

0°

90°

FIG. 15. First-order sideband height as a function of the sampleangle. The sample is shown to influence the effective dressing field,because the component of the electric field perpendicular to thesurface is reduced due to boundary conditions. The data agree withthe expected cos2 reduction in the effective intensity. The inset il-lustrates the definition of the sample angle �surface normal� for 0°and 90° with respect to the ir polarization.

LASER-ASSISTED PHOTOEMISSION FROM SURFACES PHYSICAL REVIEW A 77, 022903 �2008�

022903-11

the photoemitted electron. As the parallel component E� van-ishes here, only the perpendicular field E�=Ein cos � re-mains. For moderate laser intensities, A1 is linear in IL andtherefore follows Iin cos2 �.

Figure 16 depicts a series of photoemission spectra takenat different ir peak intensities. ir-xuv �solid lines� and xuv-only �dotted lines� at time zero as well as ir-xuv at −100 fstime delay �dashed� are shown. The −100 fs curves reflectthe influence of the space charge of the ir-induced low-energy electrons on the xuv photoelectrons around the Fermiedge. At low intensities, it results in a shift to higher energiesdue to acceleration, whereas the shape of the spectrum isunaffected. At the highest intensity shown, the space chargealso changes the shape of the spectrum. After correcting forthe space-charge shifts using the −100 fs spectra, the side-band heights A1 are determined using the fit procedure de-scribed above. The results are shown in Fig. 17. The mea-surement taken near 600 GW /cm2 is still below the damagethreshold of the surface. However, at this intensity the spacecharge created by the ir beam on the sample starts changingthe shape of the ir-xuv spectrum as compared to the xuv-onlyone, making the extraction of the sideband amplitude moredifficult. We thus used a ir-xuv spectrum taken at −100 fs as

a background spectrum for the convolution, since it showsthe same distortions due to the space-charge effect as their-xuv spectrum but does not exhibit the sidebands. This pro-cedure leads to the larger uncertainty for this data point. Ateven higher laser intensities, electrons from ATP begin tooverlap with the Fermi edge in the spectra, and bury theLAPE signature. However, such high laser intensities areonly necessary for testing the validity of the simple theoret-ical description of surface LAPE given earlier.

The laser intensity is also corrected for the sample angle,so that it corresponds to the perpendicular component of theelectric field. This corrected laser-intensity dependence isthen fit to An=Jn

2�a�I�. Here, a is a fit parameter and n=1denotes the number of absorbed or emitted ir photons. Quali-tatively, we find excellent agreement between our data andthis model. The quantitative comparison is limited by theknowledge of the actual ir beam intensity. We calculated thepeak ir intensity corresponding to the perpendicular electricfield at the surface by taking into account the sample angle.This intensity is likely to be an overestimation of the effec-tive dressing intensity for two reasons. First, the xuv beamspot size is estimated to be a significant fraction of the irbeam spot size. And second, a possible misalignment of thespatial ir-xuv overlap would decrease the effective intensity.From the kinetic energies of the electrons around the Fermiedge and the laser photon energy, the first-order sidebandamplitude is expected to peak at 540 GW /cm2. From the fitwe find the maximum of the Bessel function at960 GW /cm2, which is within our error margin for the ef-fective intensity. Note also that our highest data point has anamplitude of A1=0.30, very close to the maximum of thesquare of the first-order Bessel function of 0.348. This showsthat essentially all detected photoelectrons are dressed.

For applications such as measurement of pulse duration orsurface electron dynamics, it is desirable to use lower IRpulse intensities in the linear regime, where the cross-

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FIG. 16. Photoemission due to both ir-xuv �solid lines� and xuv-only �dotted lines� light at time zero as well as ir-xuv for a delay of−100 fs �dashed� for different ir laser intensities. The −100 fscurves show the influence of the space charge induced by the ir-induced low-energy electrons on the xuv photoelectrons around theFermi edge. At low intensities, it results in a shift to higher energiesdue to acceleration. At the highest intensity shown, the space chargealso changes the shape of the spectrum.

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120010008006004002000IR peak intensity (GW/cm

2)

FIG. 17. Extracted sideband intensity A1 as a function of theeffective ir beam peak intensity, perpendicular to the surface. Theinfluence of the sample angle has been taken into account. Thesideway intensity follows the theoretically expected square of thefirst-order Bessel function. The position of the maximum of thecurve is by about a factor of 2 higher than expected from the argu-ment of the Bessel function �Eq. �6��. This is within our experimen-tal uncertainty in the determination of the effective dressing inten-sity, because of insufficient knowledge of the spatial overlapbetween ir and xuv pulses on the sample.

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correlation A1��� directly reflects the time behavior understudy. At these laser intensities, we found LAPE to be thedominant process. The presence of space charge induces onlya small overall shift in the spectra that can be corrected for.Above-threshold photoemission can be suppressed below600 GW /cm2 by using a flat surface �42�. The excitation ofhot electrons has been found to cause significantly smallermodifications of the photoemission spectrum than LAPEeven at rather high laser intensities. However, the presence ofsuch hot electrons can be distinguished from LAPE sincetheir presence increases the average electron kinetic energyaround the Fermi edge.

In conclusion, our data show that laser-assisted photo-emission from a Pt�111� surface can be observed for ir in-tensities up to 600 GW /cm2, below what is needed to ob-serve heating, ATP, or desorption at metal surfaces �8�. Thisresult is important for applications of surface LAPE to thestudy of attosecond electron dynamics in solids and insurface-adsorbate systems.

D. Hot electrons

At high ir laser intensities �IL�5�1011 W /cm2�, a sig-nificant number of electrons within the conduction band will

a) b)

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FIG. 18. �a� Photoemission spectra around the Fermi edge for s-polarized ir light at high laser intensity �1012 W /cm2�. The electric fieldat the surface vanishes in this case, so that no dressing is expected. However, due to the absorption of ir light, a hot electron distribution isexcited, and is visible at the Fermi edge for relative time delays later than −60 fs �time zero in this measurement�. �b� Photoemission spectrafor p-polarized ir light at half the intensity applied in �a� �5�1011 W /cm2�. Hot electrons are visible at positive time delays. LAPE can beobserved at −40 fs �time zero�, clearly dominating the hot electron distribution and distinguishable by its steplike shape.

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be excited, resulting in a nonequilibrium hot electron distri-bution at the Fermi edge. The number of excited electronsdepends only on the laser fluence absorbed by the metal. Hotelectron excitation is thus expected regardless of the polar-ization, although energy coupling into the surface can vary�to some extent� with polarization. In order to observe hotelectrons—but suppress LAPE—we acquired the time seriesof photoemission spectra shown in Fig. 18�a� usings-polarized ir light at a high intensity of about 1012 W /cm2.For time delays greater than −60 fs, a slight influence of their laser light is observed in the ir-xuv spectra. However, thiseffect is considerably smaller than in the previous measure-ments with p-polarized light. We analyze these excess elec-trons in two different ways. First we subtracted the xuv-onlyspectra from the corresponding ir-xuv spectra. These differ-ence spectra show a peak above the Fermi edge stemmingfrom the excess electrons. Figure 19 shows the integratedarea of this peak versus time delay. The second approach toanalyze these data is by calculating the average kinetic ener-gies �Ekin,ir and �Ekin,xuv above the ATP distribution �i.e.,�33 eV in this case�. In Fig. 19, the solid line shows, as afunction of time delay, the normalized difference ��Ekin,ir − �Ekin,xuv � / �Ekin,xuv , i.e., the laser-induced increase of thekinetic energy. After proper scaling, the curves are shown tofollow the same characteristics: an increase in electrons �EFat −60 fs followed by an exponential decay as the time delayincreases. Since for positive time delays, the ir pulse comesfirst, it obviously serves as a pump for the process observedhere. This time behavior is fundamentally different from thecross correlation found for LAPE, and indicates the excita-tion of a comparatively long-lived hot electron distribution.

Figure 18�b� shows another time series taken withp-polarized ir light at a laser intensity of 5�1011 W /cm2,which is half the intensity used with the s-polarized lightdata discussed above. These data clearly show a LAPE signalat −40 fs, visible again as a comparably strong steplikemodification of the Fermi edge. In additions excess electronsare visible beyond the Fermi edge for time delays exceedingthe ir-xuv cross-correlation time. We again corrected for thesmall space-charge effect and then evaluated the excess elec-

trons and the kinetic energy increase �Fig. 20�. In this mea-surement, the time dependence of the excess electrons exhib-its a two-component structure. We ascribe the peak at −40 fsto LAPE. The corresponding spectrum could be fitted in theway described above. The subsequent slow decay is due tohot electrons. A fit yields a decay time of about 260 fs, inagreement with the measurement using s-polarized light. Thekinetic energy curve reflects only the hot electron contribu-tion to the excess electrons since LAPE does not change thenet kinetic energy. This shows that the slow decay can beattributed to electrons that on average gain kinetic energy,whereas the peak is due to electrons that are redistributedsymmetrically due to LAPE.

V. CONCLUSIONS AND OUTLOOK

In conclusion, we have investigated the laser-assistedphotoelectric effect from a solid surface. By illuminating aPt�111� sample simultaneously with ultrashort 1.6 and 42 eVpulses, we observed sidebands in the extreme ultravioletphotoemission spectrum. Sideband amplitudes were ex-tracted very accurately from the continuous spectra over awide range of laser intensities. Our results agree with asimple model, in which LAPE is described by xuv photo-emission followed by the interaction of the photoemittedelectron with the laser field. This strong effect can defini-tively be distinguished from other laser surface interactionphenomena, such as hot electron excitation, above-thresholdphotoemission, and space-charge acceleration. As a conse-quence, laser-assisted photoemission from surfaces promisesto be useful to extend xuv pulse duration measurements tohigher photon energies, as well as opening up femtosecond-to-attosecond time-scale electron dynamics in solid andsurface-adsorbate systems.

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FIG. 19. Excess hot electrons �dots� at the Fermi edge fors-polarized ir light. These hot electrons follow a sharp rise and slowexponential decay. The fit �dashed line� yields a lifetime of about270�60 fs. This behavior is also found for the average kineticenergy �solid line� and is consistent with expected hot electronlifetimes.

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FIG. 20. Excess hot electrons �dots� at the Fermi edge forp-polarized ir light. In this case, the excess electrons show a two-component structure. For large time delays they decay exponen-tially. The fit results in a lifetime of 260�80 fs, in agreement withthe value found for s-polarized light �270�60 fs�. Around timezero, the electron distribution exhibits a peak which is due toLAPE. The average kinetic energy, which is insensitive to LAPE,still follows the exponential decay behavior characteristic of hotelectron decay.

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ACKNOWLEDGMENTS

The authors gratefully acknowledge support for this workfrom the National Science Foundation Physics Frontier Cen-

ters Program. G.S. acknowledges support from the MaxPlanck Society. This research made use of NSF EngineeringResearch Centers Shared Facilities supported by Grant No.EEC-0310717.

�1� Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H.Kapteyn, Phys. Rev. Lett. 79, 2967 �1997�.

�2� C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M.Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz,Science 278, 661 �1997�.

�3� H. C. Kapteyn, M. M. Murnane, and I. P. Christov, Phys. To-day 58 �3�, 39 �2005�.

�4� F. Quere, S. Guizard, P. Martin, G. Petite, H. Merdji, B. Carré,J.-F. Hergott, and L. Le Déroff, Phys. Rev. B 61, 9883 �2000�.

�5� A. Rettenberger, P. Leiderer, M. Probst, and R. Haight, Phys.Rev. B 56, 12092 �1997�.

�6� S. Passlack, S. Mathias, O. Andreyev, D. Mittnacht, M.Aeschlimann, and M. Bauer, J. Appl. Phys. 100, 024912�2006�.

�7� K. Read, H. S. Karlsson, M. M. Murnane, H. C. Kapteyn, andR. Haight, J. Appl. Phys. 89, 294 �2001�.

�8� M. Bauer, C. Lei, K. Read, R. Tobey, J. Gland, M. M. Mur-nane, and H. C. Kapteyn, Phys. Rev. Lett. 87, 025501 �2001�.

�9� R. I. Tobey, E. H. Gershgoren, and M. E. Siemens et al., inUltrafast Phenomena XIV, edited by T. Kobayashi, T. Okada,T. Kobayashi, K. A. Nelson, and S. D. Silvestri �Springer-Verlag, Niigata, Japan, 2004�, p. WC3.

�10� L. Nugent-Glandorf, M. Scheer, D. Samuels, V. M. Bierbaum,and S. R. Leone, J. Chem. Phys. 117, 6108 �2002�.

�11� E. Gagnon, P. Ranitovic, A. Paul, C. Lewis Cocke, M. M.Murnane, H. C. Kapteyn, and A. S. Sandhu, Science 317,1374 �2007�.

�12� A. Weingartshofer, J. K. Holmes, G. Caudle, E. M. Clarke, andH. Krüger, Phys. Rev. Lett. 39, 269 �1977�.

�13� J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H.G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys.Rev. Lett. 73, 2180 �1994�; Phys. Rev. A 52, 1272 �1995�.

�14� M. M. Murnane, H. C. Kapteyn, and R. W. Falcone, Phys. Rev.Lett. 62, 155 �1989�.

�15� T. E. Glover, R. W. Schoenlein, A. H. Chin, and C. V. Shank,Phys. Rev. Lett. 76, 2468 �1996�.

�16� M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V.Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U.Heinzmann, and F. Krausze, Nature �London� 419, 803�2002�.

�17� P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph.Balcou, H. G. Muller, and P. Agostini, Science 292, 1689�2001�.

�18� A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E.Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A.Scrinzi, T. W. Hänsch, and F. Krausz, Nature �London� 421,611 �2003�.

�19� M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N.Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher,and F. Krausz, Nature �London� 414, 509 �2001�.

�20� R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska,

V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U.Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Na-ture �London� 427, 817 �2004�.

�21� J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, andP. B. Corkum, Phys. Rev. Lett. 88, 173903 �2002�.

�22� M. Meyer, D. Cubaynes, P. O’Keeffe, H. Luna, P. Yeates, E. T.Kennedy, J. T. Costello, P. Orr, R. Taïeb, A. Maquet, S. Düs-terer, P. Radcliffe, H. Redlin, A. Azima, E. Plönjes, and J.Feldhaus, Phys. Rev. A 74, 011401�R� �2006�.

�23� L. Miaja-Avila, C. Lei, M. Aeschlimann, J. L. Gland, M. M.Murnane, H. C. Kapteyn, and G. Saathoff, Phys. Rev. Lett. 97,113604 �2006�.

�24� A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A.Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S.Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R.Kienberger, F. Krausy, and U. Heinzmann, Nature �London�449, 1029 �2007�.

�25� T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, Nature�London� 432, 605 �2004�.

�26� P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte,and G. D. Tsakiris, Nature �London� 426, 267 �2003�.

�27� H. R. Reiss, Phys. Rev. A 22, 1786 �1980�.�28� H. G. Muller, H. B. van Linden van den Heuvell, and M. J.

Van der Wiel, J. Phys. B 19, L733 �1986�.�29� L. B. Madsen, Am. J. Phys. 73, 57 �2005�.�30� M. P. Seah and W. A. Dench, Surf. Interface Anal. 1, 2 �1979�.�31� S. Tanuma, T. Shiratori, T. Kimura, K. Goto, S. Ichimura, and

C. J. Powell, Surf. Interface Anal. 37, 833 �2005�.�32� B. Feuerbacher and R. F. Willis, J. Phys. C 9, 169 �1976�.�33� R. Haydock and M. J. Kelly, Surf. Sci. 38, 139 �1973�.�34� A. Cionga, V. Florescu, A. Maquet, and R. Taieb, Phys. Rev. A

47, 1830 �1993�.�35� A. Mönnich, J. Lange, M. Bauer, M. Aeschlimann, I. A.

Nechaev, V. P. Zhukov, P. M. Echenique, and E. V. Chulkov,Phys. Rev. B 74, 035102 �2006�.

�36� J. E. Bayfield, L. D. Gardner, Y. Z. Gulkok, and S. D. Sharma,Phys. Rev. A 24, 138 �1981�.

�37� H. R. Reiss, Phys. Rev. A 39, 2449 �1989�.�38� N. Tzoar and J. I. Gersten, Phys. Rev. B 12, 1132 �1975�.�39� F. H. M. Faisal and J. Z. Kamiński, Phys. Rev. A 56, 748

�1997�.�40� S. H. Autler and C. H. Townes, Phys. Rev. 100, 703 �1955�.�41� G. Leschik, R. Courths, H. Wern, S. Hüfner, H. Eckardt, and J.

Noffke, Solid State Commun. 52, 221 �1984�.�42� M. Aeschlimann, C. A. Schmuttenmaer, H. E. Elsayed-Ali, R.

J. D. Miller, J. Cao, Y. Gao, and D. A. Mantell, J. Chem. Phys.102, 8606 �1995�.

�43� G. Petite, P. Agostini, R. Trainham, E. Mevel, and P. Martin,Phys. Rev. B 45, 12210 �1992�.

�44� S. Backus, R. Bartels, S. Thompson, R. Dollinger, H. C.Kapteyn, and M. M. Murnane, Opt. Lett. 26, 465 �2001�.

LASER-ASSISTED PHOTOEMISSION FROM SURFACES PHYSICAL REVIEW A 77, 022903 �2008�

022903-15

�45� A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus,M. M. Murnane, and H. C. Kapteyn, Science 280, 1412�1998�.

�46� B. Shan, A. Cavalieri, and Z. Chang, Appl. Phys. B: Lasers

Opt. 74, S23 �2002�.�47� P. Siffalovic, M. Drescher, M. Spieweck, T. Wiesenthal, Y. C.

Lim, R. Weidner, A. Elizarov, and U. Heinzmann, Rev. Sci.Instrum. 72, 30 �2001�.

SAATHOFF et al. PHYSICAL REVIEW A 77, 022903 �2008�

022903-16